Even-hole-free graphs part I: Decomposition theorem

We prove a decomposition theorem for even-hole-free graphs. The decompositions used are 2-joins and star, double-star and triple-star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even-hole-free graphs. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 6–49, 2002 Part of the research was completed while Kristina Vuskovic was at the Department of Combinatorics and Optimization, University of Waterloo on an NSERC Canada International Fellowship.